(f) Show that the cartesian equation of this curve is x3 + y³ = 3xy. (g) Show that the polar equation of this curve can be written in the form 3 sec 0 tan 0 r = 1+ tan³ 0 (h) Find the area enclosed by the loop of this curve. Be careful in setting up your integrals. Provide all the details.
(f) Show that the cartesian equation of this curve is x3 + y³ = 3xy. (g) Show that the polar equation of this curve can be written in the form 3 sec 0 tan 0 r = 1+ tan³ 0 (h) Find the area enclosed by the loop of this curve. Be careful in setting up your integrals. Provide all the details.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(f) Show that the cartesian equation of this curve is x³ + y³
3xy.
(g) Show that the polar equation
this curve can be written in the form
3 sec 0 tan 0
r =
1+ tan3 0
(h) Find the area enclosed by the loop of this curve. Be careful in setting up your integrals.
Provide all the details.
Transcribed Image Text:A curve called the folium of Descartes is defined by the parametric equations
3t
x(t) =
3t2
y(t) =
1+t3 '
1+t3
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